We present observations of the Type Ia supernova 2003du
obtained with the Hobby-Eberly Telescope (HET) and report
the detection of a high-velocity component in the
\ion{Ca}{2} infrared triplet near 8000~Å, similar to
features observed in SN~2000cx and SN~2001el. This feature
exhibits a large expansion velocity (\approx 18,000
km~s-1) which is nearly constant between -7 and +2
days relative to maximum light, and disappears shortly
thereafter. Other than this feature, the spectral evolution
and light curve of SN~2003du resemble those of a normal
SN~Ia.

We consider possible origins for this high-velocity
\ion{Ca}{2} feature and find that it can be caused by a
dense shell formed when circumstellar material of solar
abundance is overrun by the rapidly expanding outermost
layers of the SN ejecta. Model calculations show that the
optical and infrared spectra are remarkably unaffected by
the circumstellar interaction and the resulting shell. In
particular, no hydrogen lines are detectable in either
absorption or emission after the phase of dynamic
interaction. The only qualitatively different features in
the model spectra are the strong, high velocity feature in
the \ion{Ca}{2} IR-triplet around 8,000~Å, and a somewhat
weaker \ion{O}{1} feature near 7,300~Å. The Doppler shift
and time evolution of these features provides an estimate
for the amount of accumulated matter and also an indication
of the mixing within the dense shell.

We apply these diagnostic tools to SN~2003du and infer that
about 2 \times 10-2M\odot of solar abundance material
may have accumulated in a shell prior to the observations.
The early light curve implies that the circumstellar
material was very close to the progenitor system, perhaps
originating in an accretion disk, Roche lobe, or common
envelope.